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C2×C5×C3⋊(C7⋊C8) #13132326

order1680
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C3⋊(C7⋊C8)
unambiguous semidirect product(C2×C3)⋊(C5×C7⋊C8)
unambiguous semidirect product(C2×C7)⋊(C5×C3⋊C8)

Splittings

derived, HallC3×C7 ⋊ C2×C5×C8
HallC3×C5×C7 ⋊ C2×C8
HallC5×C7 ⋊ C2×C3⋊C8
HallC3×C5 ⋊ C2×C7⋊C8
SylowC7 ⋊ C2×C5×C3⋊C8
SylowC3 ⋊ C2×C5×C7⋊C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5D21
commutator, hypocenterC3×C7C2×C5×C8
FrattiniC4C2×C5×D21
FittingC2×C3×C4×C5×C7C2
socle, prime radicalC22×C3×C5×C7C4
cosocleC3×C4×C7C22×C5
LCSG ▷ C3×C7
UCSC1 ◁ C2×C4×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1680

Conjugacy classes & character table

480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1680, 346);